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• W2952794445 abstract "Given $A$ and $B$ two nonempty subsets in a metric space, a mapping $T : A cup B rightarrow A cup B$ is relatively nonexpansive if $d(Tx,Ty) leq d(x,y) text{for every} xin A, yin B.$ A best proximity point for such a mapping is a point $x in A cup B$ such that $d(x,Tx)=text{dist}(A,B)$. In this work, we extend the results given in [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math., 171 (2005), 283-293] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results of best proximity points for cyclic and noncyclic relatively nonexpansive mappings in the context of Busemann convex reflexive metric spaces. Moreover, particular results are proved in the setting of CAT(0) and uniformly convex geodesic spaces. Finally, we show that proximal normal structure is a sufficient but not necessary condition for the existence in $A times B$ of a pair of best proximity points." @default.
• W2952794445 created "2019-06-27" @default.
• W2952794445 creator A5010305947 @default.
• W2952794445 creator A5069608250 @default.
• W2952794445 date "2013-06-03" @default.
• W2952794445 modified "2023-09-27" @default.
• W2952794445 title "Best proximity pair results for relatively nonexpansive mappings in geodesic spaces" @default.
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• W2952794445 hasPublicationYear "2013" @default.
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